Ferone, Vincenzo, Kawohl, Bernd ORCID: 0000-0003-2918-7318 and Nitsch, Carlo (2018). Generalized elastica problems under area constraint. Math. Res. Lett., 25 (2). S. 521 - 534. SOMERVILLE: INT PRESS BOSTON, INC. ISSN 1945-001X

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Abstract

It was recently proved in [3, 4] that the elastic energy E(gamma) = 1/2 integral(gamma)kappa(2)ds of a closed curve gamma with curvature kappa has a minimizer among all plane, simple, regular and closed curves of given enclosed area A(gamma), and that the minimum is attained only for circles. In particular, the proof used in [4] is of a geometric nature, and here we show under which hypothesis it can be extended to other functionals involving the curvature. As an example we show that the optimal shape remains a circle for the p-elastic energy integral(gamma) vertical bar kappa vertical bar(p)ds, whenever p > 1.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Ferone, VincenzoUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Kawohl, BerndUNSPECIFIEDorcid.org/0000-0003-2918-7318UNSPECIFIED
Nitsch, CarloUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-202485
Journal or Publication Title: Math. Res. Lett.
Volume: 25
Number: 2
Page Range: S. 521 - 534
Date: 2018
Publisher: INT PRESS BOSTON, INC
Place of Publication: SOMERVILLE
ISSN: 1945-001X
Language: English
Faculty: Faculty of Mathematics and Natural Sciences
Divisions: Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
ISOPERIMETRIC INEQUALITY; CURVATURE; CURVEMultiple languages
MathematicsMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/20248

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